2018•Computational Mathematics and Mathematical PhysicsRequires access

Existence Conditions of Negative Eigenvalues in the Regular Sturm–Liouville Boundary Value Problem and Explicit Expressions for Their Number

С. В. Курочкин

Abstract

Abstract For the regular Sturm–Liouville boundary value problem with general nonseparated self-adjoint boundary conditions, conditions for the existence of zero and negative eigenvalues and expressions for their number are obtained. The conditions are expresses in a closed form, and the coefficient functions of the original equation appear in these conditions indirectly through a single numerical characteristic.

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Key concepts: Mathematics, Sturm–Liouville theory, Eigenvalues and eigenvectors, Boundary value problem, Mathematical analysis, Robin boundary condition, Zero (linguistics), Self-adjoint operator